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KengaRu [80]
3 years ago
15

Larry saves 15% of his annual salary for retirement. This year his salary was $2,000 more than last year, and he saved $3,300. W

hat was his salary last year?Required to answer.
Mathematics
1 answer:
sashaice [31]3 years ago
3 0

Answer:

5,315

Step-by-step explanation:

i think thats the answer

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You have won the lottery and will receive 20 annual payments of $10,000 starting today. If you can invest these payments at 8.5%
xxTIMURxx [149]

Answer:

$102,677.20

Step-by-step explanation:

The present value of an annuity due is determined by the following expression:

PV = P+P*(\frac{1-(1+r)^{-n+1}}{r})

Where 'P' is the amount of each payment received, 'r' is the interest rate on the investment and 'n' is the number of yearly payments.

With 20 annual payments of $10,000 at a rate of 8.5%, the present value is:

PV = 10,000+10,000*(\frac{1-(1+0.085)^{-20+1}}{0.085})\\PV = 10,000+ 10,000*(9.26772)\\PV=\$102,677.20

The present value of your winnings is $102,677.20.

8 0
3 years ago
The price of a watch was increased by 7% to £1350. What was the price before the increase? Give your answer to the nearest penny
frutty [35]

Answer:

1261.68

Step-by-step explanation:

1350 = the increased watch price= 107% of the original

1350= 1.07x

1261.68224299

Check:

7% of 1261.68224299 is 88.317757

1261.68224299 + 88.317757 = 1349.9 = 1350

Round:

1261.68224299  

To the penny= to the hundreth= 1261.68

3 0
3 years ago
What is 50+_that equal420​
snow_lady [41]

Answer:

370

Step-by-step explanation:

50 + x = 420

x = 420 - 50

x = 370

6 0
3 years ago
Read 2 more answers
which expressions are equivalent to the first one? I don't understand how to determine that so please explain. Thanks!​
coldgirl [10]

9514 1404 393

Answer:

  (a) -(x+7)/y

  (b) (x+7)/-y

Step-by-step explanation:

There are several ways you can show expressions are equivalent. Perhaps the easiest and best is to put them in the same form. For an expression such as this, I prefer the form of answer (a), where the minus sign is factored out and the numerator and denominator have positive coefficients.

The given expression with -1 factored out is ...

  \dfrac{-x-7}{y}=\dfrac{1(x+7)}{y}=\boxed{-\dfrac{x+7}{y}} \quad\text{matches A}

Likewise, the expression of (b) with the minus sign factored out is ...

  \dfrac{x+7}{-y}=\boxed{-\dfrac{x+7}{y}}

On the other hand, simplifying expression (c) gives something different.

  \dfrac{-x-7}{-y}=\dfrac{-(x+7)}{-(y)}=\dfrac{x+7}{y} \qquad\text{opposite the given expression}

__

Another way you can write the expression is term-by-term with the terms in alpha-numeric sequence (so they're more easily compared).

  Given: (-x-7)/y = (-x/y) +(-7/y)

  (a) -(x+7)/y = (-x/y) +(-7/y)

  (b) (x+7)/(-y) = (-x/y) +(-7/y)

  (c) (-x-7)/(-y) = (x/y) +(7/y) . . . . not the same.

__

Of course, you need to know the use of the distributive property and the rules of signs.

  a(b+c) = ab +ac

  -a/b = a/(-b) = -(a/b)

  -a/(-b) = a/b

__

<u>Summary</u>: The given expression matches (a) and (b).

_____

<em>Additional comments</em>

Sometimes, when I'm really stuck trying to see if two expressions are equal, I subtract one from the other. If the difference is zero, then I know they are the same. Looking at (b), we could compute ...

  \left(\dfrac{-x-7}{y}\right)-\left(\dfrac{x+7}{-y}\right)=\dfrac{-y(-x-7)-y(x+7)}{-y^2}\\\\=\dfrac{xy+7y-xy-7y}{-y^2}=\dfrac{0}{-y^2}=0

Yet another way to check is to substitute numbers for the variables. It is a good idea to use (at least) one more set of numbers than there are variables, just to make sure you didn't accidentally find a solution where the expressions happen to be equal. We can use (x, y) = (1, 2), (2, 3), and (3, 5) for example.

The given expression evaluates to (-1-7)/2 = -4, (-2-7)/3 = -3, and (-3-7)/5 = -2.

(a) evaluates to -(1+7)/2 = -4, -(2+7)/3 = -3, -(3+7)/5 = -2, same as given

(b) evaluates to (1+7)/-2 = -4, (2+7)/-3 = -3, (3+7)/-5 = -2, same as given

(c) evaluates to (-1-7)/-2 = 4, different from given

3 0
2 years ago
Help me with this please (sorry for the bad picture) ​
Elenna [48]

<h2>I HOPE IT WILL HELP YOU.</h2>

THANK YOU.

<h2>^ - ^</h2>

4 0
3 years ago
Read 2 more answers
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